Squares Examples

Example 1

Find .

This isn't the square of anything from 0 through 20, so we certainly don't have it memorized. Instead, factor 2304 and see what we find. 2304 is even, so it's divisible by 2. We'll start by seeing how many 2s we can pull out. Hmm, maybe there's a "factor extractor" somewhere on that Swiss Army knife of yours.

We could easily keep pulling out more 2s. It's kind of addictive. However, we recognize that 144 is the square of 12. Therefore,

2304 = 2 × 2 × 2 × 2 × 12 × 12.

We have four factors of 2 and two factors of 12. Rearrange and group the factors so that 2304 looks like the square of something real instead of a jumbled mess that makes your gym locker look tidy (yes, including that banana from first semester):

2304 = (2 × 2 × 12)(2 × 2 × 12).

Whoa, those are the same. We can conclude that 2304 is the square of

2 × 2 × 12 = 48.

Check the answer by squaring 48 and making sure it actually does equal 2304. Sweet.